Palladium-mediated bis-arylation of inactivated and activated arenes

Article abstract of DOI:10.1080/00397910903531870

A simple synthetic protocol has been developed for the bis-arylation of unactivated and activated arenes by the implementation of a palladium-catalyzed intramolecular cyclization strategy. The activated arenes give either linearly fused or angularly fused

Full text of DOI:10.1080/00397910903531870

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Palladium-Mediated Bis-Arylation of
Inactivated and Activated Arenes
Krishna C. Majumdar a , Nirupam De a & Santanu Chakravorty a
a Department of Chemistry , University of Kalyani , Kalyani, India
Published online: 14 Dec 2010.
To cite this article: Krishna C. Majumdar , Nirupam De & Santanu Chakravorty (2010) Palladium-
Mediated Bis-Arylation of Inactivated and Activated Arenes, Synthetic Communications: An
International Journal for Rapid Communication of Synthetic Organic Chemistry, 41:1, 121-130, DOI:
10.1080/00397910903531870
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Synthetic Communications1, 41: 121–130, 2011
Copyright # Taylor & Francis Group, LLC
ISSN: 0039-7911 print=1532-2432 online
DOI: 10.1080/00397910903531870
PALLADIUM-MEDIATED BIS-ARYLATION OF
INACTIVATED AND ACTIVATED ARENES
Krishna C. Majumdar, Nirupam De, and Santanu Chakravorty
Department of Chemistry, University of Kalyani, Kalyani, India
A simple synthetic protocol has been developed for the bis-arylation of unactivated and
activated arenes by the implementation of a palladium-catalyzed intramolecular cyclization
strategy. The activated arenes give either linearly fused or angularly fused bis-cyclized
product depending upon the substitutent present on the nitrogen atom, whereas inactivated
arenes give only linearly fused product. The reaction has been carried out in two steps under
ligand-free conditions.
Keywords: Biaryl coupling; bis-cyclization; palladium acetate; pyridonaphthyridinedione; pyridoquino-
linedione
INTRODUCTION
In recent years, direct arylation has been successfully applied to intermolecular
reactions with a variety of heteroarenes,[1] arenes possessing a directing group,[2] and
for the formation of five- and six- membered rings.[3] Because of the presence of aryl–
aryl linkage in many natural products[4,5] and synthetic compounds,[6,7] a variety of
catalytic methods[8,9] has been developed for the synthesis of such biaryl compounds.
Among the various methods developed, palladium (Pd)–catalyzed intramolecular
cyclization has emerged as an efficient route for the formation of biaryls.[10–13]
Recently, we have also reported the synthesis of condensed heteroaromatic com-
pounds using biaryl-coupling reactions with Pd reagents.[14–18] Palladium-catalyzed
cyclization by the implementation of the intramolecular coupling reaction has failed
where a secondary amide was used as the starting material.[19,20] Goswami et al.[21]
reported that in the case of Pd-catalyzed reaction of iodoarylbenzamides, a small
amount of intramolecularly coupled cyclized product was formed in addition to
the symmetrical biaryl coupling product. In contrast to reports of the utilization
of electron-rich heterocycles in the direct arylation process,[22] both intra- and inter-
molecular reactions, the direct arylation of a simple aromatic ring remains a signifi-
cant challenge.[23] The use of electron-poor heterocycles, such as azines, is rare.[24,25]
Reported results in these cases are known to produce five- or six- membered ring
formation, in very poor yields and under harsh reaction conditions. Recently Leclerc
Received September 20, 2009.
Address correspondence to Krishna C. Majumdar, Department of Chemistry, University of
Kalyani, Kalyani 741235, W. B, India. E-mail: kcm_ku@yahoo.co.in
121

122
K. C. MAJUMDAR, N. DE, AND S. CHAKRAVORTY
Figure 1. Structure of nybomycin.
Figure 2. Quinolino[3,4-b][1,9]diazaphenanthrene derivative.
and Fagnou reported the intermolecular arylation of azines and diazines by exploit-
ing the transformation of these substrates on the more electron-rich azine and dia-
zine N-oxides.[25] The antibiotic nybomycin was isolated several years ago from
streptomycete cultures.[26,27] The ring system of nybomycin provides the first
naturally occurring example of a pyridoquinolone derivative (Fig. 1).
Asahara et al.[28] reported the synthesis of quinolino[3,4-b][1,9]diazaphenan-
threne derivatives (Fig. 2) by the reaction of 1-methyl-3,6,8-trinitro-2-quinolone
(TNQ) with ethoxyethene in the presence of triethyl amine in acetonitrile.
Palladium-mediated bis-biaryl coupling is an important pathway for the forma-
tion various heterocyclic compounds.[29] Recently, we reported Pd-mediated oxidat-
ive bis-cyclization for the formation of bis-benzofuran derivatives.[30] In this article,
we report our studies on the direct arylation (bis-biaryl coupling) reactions of both
electron-rich and electron-poor heterocycles for the formation of synthetically and
biologically important heterocycles. The results are important because there are lim-
ited reports highlight the bis-biarylation of either activated or unactivated arenas.[29]
RESULTS AND DISCUSSION
The requisite precursors 2a–f for our present synthesis were prepared in good to
excellent yields by the reaction between either 2-iodobenzoyl chloride with
corresponding diamine 1a–d or between N-substituted-2-bromoaniline with diacid
chloride 1e,f in dry dichloromethane in the presence of triethyl amine as a base and
dimethylaminopyridine (DMAP) as a catalyst for 3–4 h as represented in Scheme 1.

BIS-ARYLATION OF ARENES
123
Scheme 1. Reagents and conditions: (i) dry DCM, Et3N, and DMAP (cat), at rt.
Initially, we carried out Pd-catalyzed intramolecular coupling reaction of the
precursor 2a in the presence of 10 mol% Pd(OAc)2 as a catalyst with, KOAc as a base
and tetrabutylammoniumbromide (TBAB) as additive in dry dimethylformamide
(DMF) at 110 ꢀC for 3 h under a nitrogen atmosphere, and the bis-cyclized product
3a was obtained in 75% yield (Scheme 2).
We then focused our attention on standardizing the reaction conditions by con-
sidering the effect of different bases, solvents, and catalysts on the formation of the
bis-cyclized product 3a using 2a as the model substrate. Among the different bases
that were used (Cs2CO3, KOAc, K2CO3, Ag2CO3, Et3N), KOAc proved to be
superior to others. Among the various aprotic solvents (DMF, CH3CN, dioxane),
DMF was found to be the best choice. Low-boiling solvent CH3CN did not lead to
any bis-cyclized product. No bis-cyclized product was formed when the catalyst
was changed to Pd(PPh3)4, as indicated by thin-layer chromatography (TLC).
However, the bis-cyclized product was formed in a little amount when PdCl2 or
Scheme 2. Reagents and conditions: (ii) TBAB, KOAc, Pd(OAc)2, and dry DMF, at 110 ꢀC.

124
K. C. MAJUMDAR, N. DE, AND S. CHAKRAVORTY
Table 1. Optimization for 3a from 2a
Entry
Catalysta
Base
Solventb
Yield %
1
2
3
4
5
6
7
8
9
Pd(OAc)2
Pd(OAc)2
Pd(OAc)2
Pd(OAc)2
Pd(OAc)2
Pd(OAc)2
Pd(PPh3)4
PdCl2
KOAc
K2CO3
Cs2CO3
Et3N
DMF
DMF
DMF
DMF
DMF
MeCN
DMF
DMF
DMF
75
20
41
35
Ag2CO3
KOAc
KOAc
KOAc
KOAc
30
NRc
NR
22
Pd(PPh3)2Cl2
30
a10 mol % of catalyst was used in all cases.
bThe reaction was carried out at 110 ꢀC in DMF and at 85 ꢀC in MeCN.
cNR, no reaction.
Pd(PPh3)2Cl2 was used as a catalyst. The temperature plays an important role in this
reaction. The yield was reduced dramatically when the reaction was carried out below
the optimum temperature (110 ꢀC in DMF). The results are summarized in Table 1.
Substrates 2c–f gave a similar type of bis-cyclized products under the same
set of reaction conditions (Table 2). However, in the case of substrate 2b, the angu-
larly fused bis-cyclized product was obtained instead of the linearly fused
bis-cyclized product. This may be because the bulkiness of substitution in the nitro-
gen atom plays an important role in the mode of the cyclization. Because of the
more bulky character of the ethyl group than that of the methyl group, a linearly
fused product was obtained in the case of 2a instead of the angularly fused product
as in the case of 2b.
Usually, a ligand is necessary for the biaryl cyclization, but in our case all the
cyclized products were obtained under ligand-free conditions. Pyridoquinolinedione,
pyridonaphthyridinedione, and pyridoisoquinolinedione, which are important part of
various natural products, synthetic pigments, and receptors used in host–guest chemis-
try, were synthesized by various groups either by multistep[31,32] or multicomponent[28]
coupling utilizing expensive starting materials and reagents. In the present instance, we
have successfully developed a synthetic protocol for their synthesis.
In conclusion, our present method has proven to be a practical and efficient
route for direct aryaltion of both electron-rich and electron-poor heterocycles using
ligand-free conditions, providing a straightforward synthesis of biologically impor-
tant bis-diamides. Compared to other metal-catalyzed reactions, this method is
attractive in that it affords relatively complex products in good yields in two steps
from readily available starting materials.
EXPERIMENTAL
Melting points were determined in open capillaries and are uncorrected. Infra-
red (IR) spectra were recorded on a Perkin-Elmer L 120–000A spectrometer (cmax in
cmꢁ1) using liquid samples as neat liquids and solid samples in KBr disks. 1H NMR
(400-MHz) spectra were recorded on a Bruker DPX-400 spectrometer and 13C NMR
(500-MHz) spectra were recorded on a Bruker DPX-500 spectrometer in CDCl3

BIS-ARYLATION OF ARENES
125
Table 2. Results of intramolecular cyclization
Entry
Substrate
Time (h)
Product
Yield (%)
1
3
75
85
72
2
3
3.2
6
4
2
94
5
6
3.5
81
70
5
(chemical shift in d with tetramethylsiane (TMS) as internal standard. Elemental
analyses were carried out on a Perkin-Elmer 2400 series II CHN analyzer from
Kalyani University. Mass spectra were recorded on Jeol JMS600 and QTOF Micro
YA 263 instruments. Silica gel [(60–120, 230–400 mesh), Spectrochem, India] was
used for chromatographic separation. Silica gel G [E-Merck (India)] was used for
TLC. Petroleum ether refers to the fraction boiling at 60–80 ꢀC.
General Procedure for the Preparation of the Amide Precursors
Dimethylaminopyridine (DMAP, 5 mg) and Et3N (2 ml) were added to a dry
dichloromethane (20 mL) solution of 1a (300 mg, 1.8 mmol) at ice-bath temperature.

126
K. C. MAJUMDAR, N. DE, AND S. CHAKRAVORTY
2-Iodobenzoyl chloride (prepared from 2-iodobenzoic acid and thionyl chloride) in
dry DCM solution (10 ml) was added drop-wise to the reaction mixture and stirred
for 3 h at room temperature. The mixture was then washed with water (3 ꢂ 10 ml)
and brine (15 ml) and dried (Na2SO4). Evaporation of DCM gave a crude mass,
which was purified by chromatography over silica gel using petroleum ether–ethyl
acetate (7:3) to afford product 2a. Compounds 2b–d were similarly prepared. Com-
pounds 2e,f were prepared by the same procedure by the reaction between either 1e
or 1f with N-ethyl-2-bromoaniline.
Selected Data
Compound 2a. Yield: 80%; white solid; mp 121–123 ꢀC (acetonitrile–
1
petroleum ether); IR (KBr): nmax ¼ 2940, 1660 cmꢁ1, H NMR (CDCl3, 400 MHz):
dH ¼ 7.65 (d, 2H, J ¼ 6.9 Hz), 7.40 (t, 1H, J ¼ 7.6 Hz), 7.02–7.09 (m, 4H),
6.89–6.94 (m, 3H), 6.82 (t, 2H, J ¼ 7.5 Hz), 3.82 (q, 4H, J ¼ 6.9 Hz), 0.95 (t, 6H,
J ¼ 6.9 Hz); MS: m=z ¼ 624 [M]þ, Anal. calcd. for C24H22I2N2O2: C, 46.18; H,
3.55; N, 4.49%. Found: C, 46.60; H, 3.41; N, 4.45%.
Compound 2b. Yield: 85%; white solid; mp 116–118 ꢀC (DCM—petroleum
1
ether) IR (KBr): nmax ¼ 2947, 1661 cmꢁ1; H NMR (CDCl3, 400 MHz): dH ¼ 7.67
(d, 2H, J ¼ 7.6 Hz), 7.06–7.10 (m, 4H), 6.88–6.98 (m, 6H), 3.34 (s, 6H); MS: m=
z ¼ 596 [M]þ. Anal. calcd. for C22H18I2N2O2: C, 44.32; H, 3.04; N, 4.70%. Found:
C, 43.91; H, 3.09; N, 4.29%.
Compound 2c. Yield: 78%; gummy; IR (KBr): nmax ¼ 2944, 1666 cmꢁ1,
1H NMR (CDCl3, 400 MHz): dH ¼ 7.75 (d, 2H, J ¼ 7.0 Hz), 7.26–7.33 (m, 3H),
6.97 (m, 6H), 3.98 (q, 4H, J ¼ 7.0 Hz), 1.09 (t, 6H, J ¼ 7.0 Hz); MS: m=z ¼ 625
[M]þ. Anal. calcd. for C23H21I2N3O2: C, 44.18; H, 3.39; N, 6.72%. Found: C,
44.10; H, 3.48; N, 6.98%.
Compound 2d. Yield: 82%; white solid; mp 92–94 ꢀC (DCM–petroleum
1
ether); IR (KBr): nmax ¼ 2940, 1655 cmꢁ1; H NMR (CDCl3, 400 MHz): dH ¼ 7.88
(d, 1H, J ¼ 7.9 Hz), 7.73–7.75 (m, 2H), 7.44 (t, 2H, J ¼ 7.0 Hz), 7.30–7.34 (m, 4H),
7.09–7.13 (t, 2H, j ¼ 7.5 Hz), 6.94–7.01 (m, 1H), 3.65 (q, 4H, J ¼ 7.2 Hz), 0.94 (t,
6H, J ¼ 7.2 Hz). MS: m=z ¼ 624 [M]þ, Anal. calcd. for C24H22I2N2O2: C, 46.18; H,
3.55; N, 4.49%. Found: C, 46.55; H, 3.52; N, 4.26%.
Compound 2e. Yield: 74%; gummy; IR (KBr): nmax ¼ 2945, 1653 cmꢁ1, 1H
NMR (CDCl3, 400 MHz): dH ¼ 7.50–7.51 (m, 3H), 7.34 (d, 1H, J ¼ 7.9 Hz),
7.13–7.15 (m, 3H), 7.02–7.05 (m, 3H), 6.90–6.94 (m, 2H), 4.17 (q, 2H, J ¼ 7.1 Hz),
3.50 (q, 2H, J ¼ 7.1 Hz), 1.16 (t, 6H, J ¼ 7.1 Hz); MS: m=z ¼ 530 [M]þ, 532
[M þ 2]þ, Anal. calcd. for C24H22Br2N2O2: C, 54.36; H, 4.18; N, 5.28%. Found: C,
54.40; H, 4.17; N, 5.08%.
Compound 2f. Yield: 78%; white solid; mp 136–138 ꢀC (acetonitrile–
1
petroleum ether) IR (KBr): nmax ¼ 2943, 1652 cmꢁ1; H NMR (CDCl3, 400 MHz):
dH ¼ 7.50 (d, 1H, J ¼ 7.7 Hz), 7.33–7.45 (m, 4H), 7.20 (d, 1H, J ¼ 7.1 Hz),
7.13–7.18 (m, 2H), 7.03–7.08 (m, 2H), 6.89 (d, 1H, J ¼ 7.80 Hz), 4.25 (q, 1H,
J ¼ 7.0 Hz), 4.12 (q, 1H, J ¼ 7.0 Hz), 3.47 (q, 1H, J ¼ 7.0 Hz), 3.36 (q, 1H,

BIS-ARYLATION OF ARENES
127
J ¼ 7.0 Hz), 1.18 (t, 3H, J ¼ 7.0 Hz), 1.15 (t, 3H, J ¼ 7.0 Hz); 13C NMR (CDCl3,
75 MHz): dc ¼ 167.0, 166.8, 152.0, 151.9, 141.1, 141.0, 136.3, 136.2, 133.2, 133.0,
132.3, 131.7, 129.0, 128.9, 127.7, 127.5, 123.5, 123.2, 123.0, 44.1, 43.9, 12.5, 12.3.
MS: m=z ¼ 531 [M]þ, 533 [M þ 2]þ. Anal. calcd. for C23H21Br2N3O2: C, 52.00; H,
3.98; N, 7.91%. Found: C, 51.69; H, 3.95; N, 7.71%.
General Procedure for the Intramolecular Heck Cyclization
A mixture of compound 2a (100 mg, 0.16 mmol), anhydrous potassium acetate
(31 mg, 0.32 mmol), tetrabutylammonium bromide (103 mg, 0.32 mmol), and
Pd(OAc)2 (3.5 mg, 10 mol%) was heated in dry DMF (5 mL) under a nitrogen atmos-
phere at 110 ꢀC for 3 h with continuous stirring. After completion of the reaction as
monitored by TLC, the reaction mixture was cooled, and water (5 ml) was added.
This was then extracted with CH2Cl2 (3 ꢂ 10 ml). The CH2Cl2 extract was washed
with water (3 ꢂ 10 ml), followed by brine (10 ml). The organic layer was dried
(Na2SO4). Evaporation of CH2Cl2 furnished a crude mass, which was purified by
column chromatography over silica gel. Elution of the column with petroleum
ether–ethyl acetate (3:2) afforded the product 3a. Similarly, other substrates 2b–f
were similarly subjected to the reaction under the same reaction conditions to give
products 3b–f.
Selected Data
Compound 3a. Yield: 75%; white solid; mp 280–282 ꢀC (DCM–petroleum
ether); IR (KBr): nmax ¼ 2948, 1658, 1610 cmꢁ1
;
1H NMR (CDCl3, 400 MHz):
dH ¼ 9.09 (s, 1H), 8.54 (d, 2H, J ¼ 7.9 Hz), 8.35 (d, 2H, J ¼ 8.1 Hz), 7.78 (t, 2H,
J ¼ 7.5 Hz), 7.57 (d, 2H, J ¼ 7.5 Hz), 7.27 (s, 1H), 4.49 (q, 4H, J ¼ 7.0 Hz); 1. 47 (t,
6H, J ¼ 7.0 Hz). 13C NMR (CDCl3, 125 MHz): dc ¼ 161.2, 137.9, 133.0, 132.6,
129.0, 127.7, 125.0, 121.0, 118.3, 114.5, 99.9, 37.8, 12.5. HRMS: calcd for
C24H20N2O2: 369.1563 [M þH]; found: 369.1598 [M þH].
Compound 3b. Yield: 85%; white solid; mp 291–293 ꢀC (DCM–petroleum
ether); IR (KBr): nmax ¼ 2945, 1660, 1607 cmꢁ1
;
1H NMR (CDCl3, 400 MHz):
dH ¼ 8.53 (d, 1H, J ¼ 8.0 Hz), 8.48 (d, 1H, J ¼ 7.7 Hz), 8.30 (d, 1H, J ¼ 8.8 Hz),
8.21 (d, 1H, J ¼ 8.0 Hz), 7.85 (d, 1H, J ¼ 8.0 Hz), 7.78 (t, 1H, J ¼ 7.5 Hz), 7.67
(t, 1H, J ¼ 7.7 Hz), 7.55–7.62 (m, 2H), 7.33 (d, 1H, J ¼ 8.8 Hz), 3.86 (s, 3H), 3.41
(s, 3H); 13C NMR (CDCl3, 75 MHz): dc ¼ 164.5, 161.6, 140.1, 137.9, 133.3, 132.9,
132.4, 131.4, 128.6, 128.1, 127.8, 127.7, 109.4, 42.3, 30.4; MS: m=z ¼ 340 [M]þ, Anal.
calcd. for C22H16N2O2: C, 77.63; H, 4.74; N, 8.23%. Found: C, 78.01; H, 4.80;
N, 8.42%.
Compound 3c. Yield: 72%; gummy; IR (KBr): nmax ¼ 2940, 1657, 1601 cmꢁ1
;
1H NMR (CDCl3, 400 MHz): dH ¼ 8.72 (s, 1H), 8.44 (d, 2H, J ¼ 7.8 Hz), 7.99 (d, 2H,
J ¼ 8.0 Hz), 7.68 (t, 2H, J ¼ 7.7 Hz), 7.44 (t, 2H, J ¼ 7.6 Hz), 4.56 (q, 4H, J ¼ 6.8 Hz),
1.31 (t, 6H, J ¼ 6.8 Hz). MS: m=z ¼ 369 [Mþ], Anal. calcd. for C23H19N3O2: C, 74.78;
H, 5.18; N, 11.37%. Found: C, 74.75; H, 5.20; N, 11.16%.

128
K. C. MAJUMDAR, N. DE, AND S. CHAKRAVORTY
Compound 3d. Yield: 94%; white solid; mp 144–146 ꢀC (acetonitrile–
petroleum ether); IR (KBr): nmax ¼ 2945, 1655, 1604 cmꢁ1
;
1H NMR (CDCl3,
400 MHz): dH ¼ 8.49 (d, 1H, J ¼ 7.8 Hz), 8.23 (d, 1H, J ¼ 7.8 Hz), 8.19 (d, 1H,
J ¼ 8.2 Hz), 7.71 (t, 1H, J ¼ 7.6 Hz), 7.59 (d, 1H, J ¼ 7.6 Hz), 7.43 (d, 2H, J ¼ 8.1 Hz),
7.22 (d, 1H, J ¼ 7.7 Hz), 7.09 (t, 1H, J ¼ 7.9 Hz), 6.78 (d, 1H, J ¼ 7.7 Hz), 5.02 (q, 1H,
J ¼ 6.9 Hz), 4.78 (q, 1H, J ¼ 7.0 Hz), 3.90 (q, 1H, J ¼ 7.1 Hz), 3.46 (q, 1H,
J ¼ 7.0 Hz), 1.30 (t, 3H, J ¼ 6.9 Hz), 1.16 (t, 3H, J ¼ 7.2 Hz);13C NMR (CDCl3,
75 MHz): dc ¼ 162.9, 144.1, 137.5, 133.4, 133.1, 132.4, 129.6, 129.3, 128.6, 128.5,
128.2, 127.9, 125.9, 123.5, 123.2, 122.0, 121.7, 46.1, 41.4, 14.1, 12.7; MS: m=
z ¼ 368 [Mþ]. Anal. calcd. for C24H20N2O2: C, 78.24; H, 5.47; N, 7.60%. Found:
C, 78.57; H, 5.93; N, 7.21%.
Compound 3e. Yield: 81%; white solid; mp 273–275 ꢀC (DCM-petroleum
ether); IR (KBr): nmax ¼ 2944, 1652, 1602 cmꢁ1
;
1H NMR (CDCl3, 400 MHz):
dH ¼ 9.71 (s, 1H), 9.11 (s, 1H), 8.50 (d, 2H, J ¼ 7.8 Hz), 7.60 (t, 2H, J ¼ 7.7 Hz),
7.45 (d, 2H, J ¼ 8.4 Hz), 7.36 (t, 2H, J ¼ 7.6 Hz), 4.45 (q, 4H, J ¼ 7.0 Hz), 1.42 (t,
6H, J ¼ 7.0 Hz); MS: m=z ¼ 368 [Mþ], Anal. calcd. for C24H20N2O2: C, 78.24; H,
5.47; N, 7.60%. Found: C, 78.03; H, 5.46; N, 7.56%.
Compound 3f. Yield: 70%; white solid; mp 267–269 ꢀC (DCM—petroleum
ether); IR (KBr): nmax ¼ 2944, 1652, 1602 cmꢁ1, 1H NMR (CDCl3, 400 MHz):
dH ¼ 8.13 (s, 1H), 7.64 (d, 2H, J ¼ 7.8 Hz), 7.47 (d, 2H, J ¼ 7.6 Hz), 7.42 (d, 2H,
J ¼ 8.2 Hz), 7.36 (d, 2H, J ¼ 8.2 Hz), 4.45 (q, 4H, J ¼ 7.0 Hz); 1.41 (t, 6H, J ¼ 7.0 Hz);
MS: m=z ¼ 369 [Mþ], Anal. calcd. for C23H19N3O2: C, 74.78; H, 5.18; N, 11.37%.
Found: C, 74.85; H, 5.12; N, 11.25%.
ACKNOWLEDGMENT
We thank the Council of Scientific and Industrial Research (CSIR) (New
Delhi) and the Department of Science and Technology (New Delhi) for financial
assistance. Two of us (S. C. and N. D.) are grateful to the CSIR and the University
Grants Commission, respectively, for fellowships.
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